To vertically stretch the parent function \( f(x) = x^3 \) by a factor of 3, we use the transformation formula \( y = kf(x) \), where \( k \) is the stretching factor. In this case, \( k = 3 \).
So, the new function will be:
\[ y = 3f(x) = 3x^3 \]
Now we can calculate the values for different \( x \) values. We already have \( x = 0 \):
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For \( x = 0 \): \[ y = 3(0^3) = 3(0) = 0 \]
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For \( x = 1 \): \[ y = 3(1^3) = 3(1) = 3 \]
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For \( x = 2 \): \[ y = 3(2^3) = 3(8) = 24 \]
Now we can fill in the table:
\[ \begin{array}{|c|c|} \hline x & y = kf(x) = 3x^3 \ \hline 0 & 0 \ 1 & 3 \ 2 & 24 \ \hline \end{array} \]
So the completed table is:
\[ \begin{array}{|c|c|} \hline x & y = 3x^3 \ \hline 0 & 0 \ 1 & 3 \ 2 & 24 \ \hline \end{array} \]
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